Rupam Barman

most citedOn the Monogenity of Polynomials with Non-Squarefree Discriminants

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math.NT2026

Explicit hypergeometric modularity of certain weight two and four Hecke eigenforms

Sipra Maity, Rupam Barman

Recently, Allen \emph{et al.} developed the Explicit Hypergeometric Modularity Method (EHMM) that establishes the modularity of a large class of hypergeometric Galois representatio…

math.NT2026

Arithmetic Aspects of Number Fields Generated by Polynomial Families

Rupam Barman, Anuj Jakhar, Ravi Kalwaniya +1

Let $f (x) = (x^{k} + c)^{m} - a x^{n} \in Z [x]$ be an irreducible polynomial over $Q$ , where $k, m, n \in N$ with $k m > n$ , and let $K = Q (θ)$ , where $θ$ is a ro…

math.NT2026

On the discriminant and index of a certain class of polynomials

Rupam Barman, Anuj Narode, Vinay Wagh

Let $f (x) = (x^{2} + 1)^{n} - a x^{n} \in Z [x]$ and assume $f (x)$ is irreducible. Let $θ$ be a root of $f (x)$ , set $K = Q (θ)$ , and denote by $Z_{K}$ the rin…

math.NT2026

On Monogeneity of reciprocal polynomials

Rupam Barman, Anuj Narode, Vinay Wagh

Let $Z_{K}$ denote the ring of integers of the number field $K = Q (θ)$ , where $θ$ is a root of the monic irreducible polynomial $f (x) \in Z [x]$ . We say tha…

math.NT2025★ 1 cited

On the Monogenity of Polynomials with Non-Squarefree Discriminants

Rupam Barman, Anuj Narode, Vinay Wagh

In 2012, for any integer $n \geq 2$ , Kedlaya constructed an infinite class of monic irreducible polynomials of degree $n$ with integer coefficients having squarefree discriminants.…